This paper describes an implicit numerical model for compositional simulation of single-porosity and dualporosity oil or gas condensate reservoirs. A 3-component equation-of-state compositional approach is proposed as a desirable alternative to extended black oil modelling, requiring little more computing time than the latter. The approach is illustrated for an actual near-critical volatile oil reservoir. A simple method for reducing implicit formulation time truncation error is described and illustrated. A new bottomhole constraint function is described for better preservation of production well target rates in compositional models. A new matrix-fracture transfer formulation including matrix-fracture diffusion is presented for the dual-porosity description; its accuracy is examined in connection with several test problems where correct results are available from single-porosity simulation. Results are discussed for a 3D 600-block simulation of a highly fractured near-critical volatile oil reservoir.